Mezzo...

Dear Jacques,

On 12.05.2010, at 17:27, Jacques Dudon wrote:
> [..] you should definitively register [..] I did it without problem.

Ah, great, I will check it out.

> I have to prepare some concerts and will less disponible for 1 month,
> so I hope you are on a good tracks now with your Ethno tunings.

Sorry that this discussion went on for so long. It is only, I would like to use Strasheela to create these demos, because then I could use them in other contexts as well (e.g., as examples in some publication). If there would be (some close approximation of) 1/4-comma meantone with a long enough chain of fifths available, then I could start right away. The reason is that Strasheela already supports 31-TET very well (e.g., with a large database of chords/scales, rules on harmony and counterpoint etc.), and so it "knows" all the interval relations of 1/4-comma meantone.

As I said, I am currently working towards Strasheela support for arbitrary regular temperaments, so I could model the interval relations of many of your tunings in Strasheela. However, it takes some additional time, and there are currently so many other things to do... On the other hand, adding support for arbitrary regular temperaments is certainly worth its time and I am already close :)

> It seems we had some misunderstanding with Mezzo, that you did not
> notice was mentionned in the scl file of Appalachian ... ?

Sorry, I did not search all scl files for some mentioning of of the word "Mezzo" :) I checked it right now: so, Mezzo is a close approximation of 1/4-comma meantone after all.

Sorry for repeating this question, but could this tuning be extended into a chain of 23 fifths (i.e. 24 tones), so that more 7-limit intervals are available? It would save me a couple of days to actually start creating 7-limit demos.

> Will try to answer later to your last messages on the TL as I can
> suggest another super great fractal generator for 7-limit, which is
> what you would need in fact as giving priority to 7 over 5 would be
> more logical.

Thank you, and sorry for taking so much of your time in this matter.

Best wishes,
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586219
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

--- In tuning@yahoogroups.com, Torsten Anders <torsten.anders@...> wrote:

> publication). If there would be (some close approximation of) 1/4-
> comma meantone with a long enough chain of fifths available, then I
> could start right away. The reason is that Strasheela already supports
> 31-TET very well (e.g., with a large database of chords/scales, rules
> on harmony and counterpoint etc.), and so it "knows" all the interval
> relations of 1/4-comma meantone.

The difference between my 5/23 comma version which Jacques said was acceptable under the rules and 1/4 comma or 31et is not so great that it should cause you any concern about your database.

Torsten wrote :

(Jacques) :
> > It seems we had some misunderstanding with Mezzo, that you did not
> > notice was mentionned in the scl file of Appalachian ... ?
>
> Sorry, I did not search all scl files for some mentioning of of the
> word "Mezzo" :) I checked it right now: so, Mezzo is a close
> approximation of 1/4-comma meantone after all.

You were the first one to mention "Appalachian" and its recurrent sequence as a tuning you were interested in :
> Your Scala files state that, for example, the file N_America/
> appalachian.scl is a recurrent series. The tuning is defined as
> follows (I am copying the whole file including the comments here).

And my answer of the 27th of april explained everything about that tuning and its recurrent sequence, which is Mezzo, and how close it is to the 1/4 syntonic comma meantone.

> Sorry for repeating this question, but could this tuning be extended
> into a chain of 23 fifths (i.e. 24 tones), so that more 7-limit
> intervals are available? It would save me a couple of days to actually
> start creating 7-limit demos.

There is a mystery here... I think I answered about half a dozen of times yes, and explained how to do it ! I offered you two solutions :
1) transposition of the whole scale by 125/128, this extends to 24 tones.
2) or if it's simpler for you or for Strasheela, using the Mezzo generator
1.495352392466 = 696.5826088 c. as many times as you want.
Can you write these scala files, or do you want me to do it for you ?
And I said also that 10 generators will approximate the 7th harmonic :
= by 965.826088 c., or 3 c. less than 7/4.

Now if you would rather use 31-TET, you should do it !
I don't know exactly what you want to do, and my advise might not be useful, but if you plan to make use of 7-limit harmonies and you have no precise idea of the meantone you want to use, what I would suggest is to give priority to 7 over 5. I have plenty of eq-b meantones that play with 7, and for many reasons the more useful ones approximate 7/4 with lower, never with higher intervals.

Close to 31-edo are :
Heptapand x^10 = 96 - 8x^4 > 696,81497441532 c.
Saptendre x^10 = 8x + 44 > 696.77164940052 c.

Closer to 1/4 syntonic there is
Sapnat x^10 = 16x + 32 > 696.65567529288 c.

Then perhaps the most terrific -c and eq-b meantone playing with 7 would be
Saprad x^10 = 32x + 8 > 696.407171331 c.

And I maintain that close to Golden,
Tara x^4 = x + 7/2 > 696.14304361824 c.
is very special as it bridges 5 and 7, but might be a little more complex to use if you're not familiar with differential coherence - and obviously, transposition by 7/4 is obviously the secret here.

One more to bridge 7 and 5, close to 50-edo :
Pandore x^9 = 64 - 8x3 > 696,02379131532 c.

- - - - - - - - -
Jacques

Dear Jacques,

sorry, I certainly did not mean to annoy you.

On 13.05.2010, at 22:59, Jacques Dudon wrote:
> There is a mystery here... I think I answered about half a dozen of > times yes, and explained how to do it ! I offered you two solutions :
> 1) transposition of the whole scale by 125/128, this extends to 24 > tones.

Ah, using the factor 125/128 is a different matter indeed! Before you were suggesting multiplying by just 5 (see copies at end of this mail), and I therefore wondered whether that would not lead to many tones which are in the tuning already.

Anyway, as I told you this morning I now have support for arbitrary regular temperaments in Strasheela. As a start today I toyed with simple 5-limit chord progressions for 22 shrutis in schismatic temperament, will soon map that to your coherent_shrutis.scl :)

Best wishes,
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586219
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

On 01.05.2010, at 23:33, jacques.dudon wrote:
> > > Since my "Mezzo" version uses
> > > transpositions by 5, it should be easy to extend it the same way > to
> > > 19 or even 24 tones to fit in the Ethno mappings.
[skip]
> I was just talking of multiplications by 5 here, I am sure you can > do that !

--- In tuning@yahoogroups.com, Torsten Anders <torsten.anders@...> wrote:
>
> Dear Jacques,
>
> sorry, I certainly did not mean to annoy you.

You're welcome to ask any question, I just want to make sure that my answers can help.

> On 13.05.2010, at 22:59, Jacques Dudon wrote:
> > There is a mystery here... I think I answered about half a dozen of
> > times yes, and explained how to do it ! I offered you two solutions :
> > 1) transposition of the whole scale by 125/128, this extends to 24 tones.
>
> Ah, using the factor 125/128 is a different matter indeed! Before you
> were suggesting multiplying by just 5 (see copies at end of this
> mail),

Yes, I said multiplications like "Appalachian" does already = 5> 25 > 125 > ...
and I mentionned transpo of the 12 tones by 125/128 before also, just to be sure you catch it. May be the explanation is that you don't read or understand my answers very well.

and I therefore wondered whether that would not lead to many
> tones which are in the tuning already.

Since there are already two near-7/4 intervals in the 12 tones, it sure does for 2 of them. And it's quite logical that by extending a meantone over 12 tones you may pass by near 19 and 31 tones divisions.
With 24 tones, you will have I guess a 19 + 5 structure somehow.
The best thing is to try it ! Then either discard the 5 doubles or add 7 more for 31 if you want DE divisions. I hope someone will have the good idea to test if the Ethno update accepts any user mapping now, such as 19 or 31.

> Anyway, as I told you this morning I now have support for arbitrary
> regular temperaments in Strasheela.

If it supports 31-ET, it should work as well with any meantone around in a large range. Then some of the "7-limit" Eq-b generators I sent you yesterday would give the best results I guess.

As a start today I toyed with
> simple 5-limit chord progressions for 22 shrutis in schismatic
> temperament, will soon map that to your coherent_shrutis.scl :)

Good idea !

> Best wishes,
> Torsten
>
Best wishes,
- - - - - -
Jacques

> Torsten Anders
> Interdisciplinary Centre for Computer Music Research
> University of Plymouth
> Office: +44-1752-586219
> Private: +44-1752-558917
> http://strasheela.sourceforge.net
> http://www.torsten-anders.de
>
>
>
> On 01.05.2010, at 23:33, jacques.dudon wrote:
> > > > Since my "Mezzo" version uses
> > > > transpositions by 5, it should be easy to extend it the same way
> > to
> > > > 19 or even 24 tones to fit in the Ethno mappings.
> [skip]
> > I was just talking of multiplications by 5 here, I am sure you can
> > do that !